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Ship Hydrodynamics, Ship Propeller Acoustics and Cavitation.

Dr.l.noordzij@leennoordzij.nl

www.leennoordzij.me

Content Introduction. ........................................................................................................................................ 1

The Cavitation Tunnel. ........................................................................................................................ 2

The Depressurized Towing Tank.......................................................................................................... 4

Cavitation and Cavitation Inception. ................................................................................................... 7

Design and testing of marine propellers. ............................................................................................ 8

Special topics. ...................................................................................................................................... 9

Literature. ............................................................................................................................................ 9

Introduction. Before a new built ship is transferred to the operator test trials will be run at high sea to find

out whether or not the new ship complies with the specifications. For example: verify the

contracted speed power by speed trials.

One of the important issues is cavitation on the propulsion system: the ship propeller.

Cavitation cannot always be prevented so you want to control it by design.

The designer and shipbuilder have made predictions of the type and amount of cavitation.

This is usually tested at model scale in a testing facility like MARIN(www.marin.nl) .

At the end of the day the type and intensity of cavitation has to be tested at high sea in

order to find out whether or not reality is within the margin of the allowable predictions.

Below some videos are shown of so-called high sea testing. The videos are recorded from a

view through a window in the stern of the top of the propeller. Vortex cavitation is shown.

Click on the link:

https://leennoordzij.files.wordpress.com/2015/01/full-scale1.mpg

Part of the rudder is shown.

A view from aside can be seen by clicking on the link:

https://leennoordzij.files.wordpress.com/2015/01/full-scale11.mpg

Cavitation observation such as shown in these videos are conducted already for several

decades. These observations are essential to find out about noise and dynamic pressures

produced by the cavitating propeller and whether or not a particular type of cavitation

creates erosion of the propeller. By the way, nowadays to make observations windows in the

stern are no longer necessary. By means of a small hole in the hull the observations can be

made.

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First and for all a model of the propeller is tested on laboratory scale. This can be done in a

so-called cavitation tunnel and/ or a depressurized towing tank.

The Cavitation Tunnel. Let us take a closer look at cavitation.

Cavitation can be categorized schematically into:

- Sheet cavitation;

- Bubble cavitation and

- Vortex cavitation.

Here a typical example of sheet cavitation is

shown. The model propeller shown is specially

designed for this type of cavitation.

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This model propeller shows

bubble cavitation.

The above model propeller displays vortex cavitation.

No examples of supercavitating are shown here. With supercavitating the sheet cavity on the

propeller blade stretches in chord wise direction beyond the trailing edge of the propeller

blade.

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Research in testing facilities is aimed to design a propeller showing allowable cavitation on

full scale. In order to conduct test in a meaningful way test has to be done under full scale

conditions. This condition can only partially be fulfilled. I come to that later on.

In the old days model test where don in the open air. Than the conditions to test cavitation

are not correctly scaled. To this end a cavitation tunnel is used.

In the above picture a cavitation tunnel is shown. This is a closed circuit in which the water

flow and pressure can be varied. These type of facility has created a considerable insight in

cavitation erosion.

Through clicking on the link below some observations in a cavitation tunnel are show:

https://leennoordzij.files.wordpress.com/2015/01/part2.mpg

In this video a cavitating hydrofoil and two cavitating model propellers are subsequently

shown.

Cavitation inception research is extensively reported in Kuiper(1981, 2012).

The Depressurized Towing Tank. However, it is not just erosion. What has also to be tested are the vibrations induced on the

ship’s hull by the dynamic behaviour of cavitation. To this end a Depressurized Towing Tank

has been developed in the Netherlands by MARIN. The tank is schematically shown below:

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The ship model is displayed below the red structure. Model with a length of 12 meters can

be tested. The width of the tank is 18 meters, the length is about 240 meters and the height

is 8 meters. The pressure can be lowered by a factor of 40.

To give you an idea about the size an outside picture is shown below.

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In this testing facility a completely scaled model can be tested the cavitating propeller

included. A video of the propeller can be observed by clicking on the link:

https://leennoordzij.files.wordpress.com/2015/01/model.avi

The recording has been made from inside the ship model.

However not all the hydrodynamical scale rules are complied with. This was one of the

reasons to construct a testing facility as the Depressurized Towing Tank shown above. With

such a facility there is compliance with two hydrodynamical parameters: the Froude number

and the cavitation index. In this way predictions for prototype flow, i.e. full scale, have been

improved. However, Reynolds number similarity is not obtained.

Nevertheless, experienced testers are able to predict rather accurately on basis of the test

results the performance of the ship in full scale. This is supported by a lot of data created

with full scale testing and trials.

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Cavitation and Cavitation Inception. Cavitation basically is a non-stationary process. Consequently inception of cavitation is a

subject of great importance to propeller design. In Kuiper(1981) a broad overview is

presented.

Inception is strongly influenced by nuclei, e.g., tiny gas bubbles and/or particulate matter. In

Noordzij and Cruijff a brief overview on nuclei and nuclei measurement is presented.

As mentioned, nuclei can influence cavitation inception. This is important in a circulating

water tunnel(Bernd, 1973) as well as in experiments without moving water(Noordzij 1976).

In the latter experiments use have been made of additional seeding of tiny gas bubbles by

means of electrolysis.

The above results are promising. As indicated in the legenda, the stabilizing effect of

additional bubbles is clearly demonstrated.

Consequently you want to know the size and number of nuclei. Keller(1973) developed an

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optical technique for determining the nuclei spectra. Like Bernd, Keller concluded the

number and size of the nuclei in water are dependent on the history of the particular water

and on its content of contaminating particles.

Keller concluded cavitation inception to be strongly affected by the nuclei content. This is of

particular interest when a critical level for inception of a nuclei spectrum under proto type

circumstances could be indicated. Then the critical level for testing facilities can be

calculated and set. Since knowing the critical proto type spectrum a critical level for model

testing can be meaningfully hypothesised. What could such a hypothesis look like?

The hypothesis is: to obtain equal cavitation inception susceptibility for both proto type(full

scale) as well as laboratory flow the encounter frequency with nuclei has to be the same for

both types of flow. (Nota bene: Kuiper mentioned encounter frequency in Cavitation in Ship

Propulsion. Kuiper dealt basically with dynamics of the cavitation nucleus: a tiny gasbubble).

This will result in an expression for the number density of the nuclei, be it particulate or tiny

bubbles, as a function of the scaling parameter 𝜆. Let the number density, i.e. the number of

nuclei per 𝑚3 say, to be 𝑛.

A typical distance for the nuclei is:

𝛬 = 𝑛−1/3. (1)

Then, a so-called encounter frequency for the propeller and the nuclei can be defined as 𝑉

𝛬, (2)

where 𝑉 is a typical velocity for the propeller, 𝜔𝐷/2 say. Here 𝜔 is the angular frequency

and 𝐷 the diameter of the propeller.

Now let us define the dimensionless frequency 𝑁𝑜 =𝑉

𝜔𝛬. (3)

Then the basic assumption is this number 𝑁𝑜 to be a constant. So :

(𝑉

𝜔𝛬)𝑚 = (

𝑉

𝜔𝛬)𝑓𝑠 , (4)

where subscripts 𝑚, 𝑓𝑠 denote model and full scale respectively.

Usually for model testing Froude number is a constant. With model scale 𝐷𝑚

𝐷𝑓𝑠=

1

𝜆, where 𝐷 is

typical length scale, the diameter of the propeller say.

We rewrite (4) : (𝑉𝐷

𝜔𝐷𝛬)𝑚 = (

𝑉𝐷

𝜔𝐷𝛬)𝑓𝑠. (5)

Since we keep the Froude number to be constant we have: 𝑉𝑚

𝑉𝑓𝑠=

(𝜔𝐷)𝑚

(𝜔𝐷)𝑓𝑠= 𝜆−1/2. Plugging

(1), and the Froude scaling into (5) we obtain: 𝑛𝑚 = 𝜆3𝑛𝑓𝑠. (6)

So this 𝑁𝑜 number is telling us the nuclei density in laboratory testing need to be much

larger than in prototype flow.

Design and testing of marine propellers. Geopolitics plays a special role in the world of marine propellers. Navy surface vessels have

been surveyed by submarines for more than 100 years. Nowadays(2016) submarines play an

ever increasing role in see bound strategies of the superpowers. Detecting submarines is an

ever interesting issue.

Detecting submarines has been done sensors measuring the noise produced by the

submarines. Noise created on-board by the diesel-electric powering system and noise

created out-board by the flow around the submarine. One of the main sources of this flow

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noise is created by the propeller. We will focus on the hydrodynamics of the propeller. A

non-cavitating propeller creates noise generated by the turbulent flow around the propeller.

This noise is amplified when the propeller starts to cavitate. In the fore going sections

various typed of cavitation are shown. Every type has its particular acoustic fingerprint.

Consequently propeller design is a major tool in reducing noise produced by the propeller

(Noordzij, et al).

As mentioned before, to optimize a propeller design testing on a certain model scale and

CFD are important tools. To make meaningful predictions with help of model scale testing

there are certain conditions for such a testing facility. Two testing facilities are mentioned in

the fore going sections. In Noordzij and Van der Kooij some ideas have been discussed

based on the far field acoustics of a cavitating propeller.

Special topics. In The Economist section on Science and Technology(January 21st 2017) a particular example

of supercavitating is discussed. It is about a submerged weapon: a kind of torpedo. Super

cavitation is taken advantage of in order. Due to supercavtation the torpedo has a very low

hydrodynamic drag.

Literature. Bernd, L. H., Gas Nuclei, Surface Films and Turbulent Dissolving as Related to Cavitation

Inception, Proceedings, IUTAM Symposium Non-Steady Flow of Water at High Speeds

Leningrad 1971, (ed. L.I. Sedov and G. Y. Stepanov), Moskow, Nauka, 1973.

Keller, A. p., The Influence of the Cavitation Nuclei Spectrum on Cavitation Inception.

Investigated with a scattered light counting method. Proceedings, IUTAM Symposium Non-

Steady Flow of Water at High Speeds Leningrad 1971, (ed. L.I. Sedov and G. Y. Stepanov),

Moskow, Nauka, 1973.

Kuiper, G., Cavitation Inception On Ship Propeller Models, Veenman, 1981.

Kuiper, G., Physics of Cavitation: Cavitation Inception. Cavitation in ship propulsion,

www.ocw.tudelft.nl , 2012.

Noordzij, L., Some Experiments on Cavitation Inception with Propellers in the NSMB-

Depressurized Towing Tank, Journal of International Shipbuilding Progress, Vol. 23, 1976.

Noordzij, L., Cruijff, H. J., Introductory nuclei spectra measurements in the NMSB-

Depressurized Towing Tank, Journal of International Shipbuilding Progress, Vol. 25, 1978.

Noordzij, L., Van Oossanen, P. and A. M. Stuurman, Radiated Noise of Cavitating Propellers,

Proceedings, Symposium on Noise and Fluid Engineering, ASME Winter Annual Meeting,

Atlanta, Georgia, Dec. 1977.

Noordzij, L., Van der Kooij, J., Hydro- Acoustics of a Cavitating Screw Propeller; Far-Field

Approximations, Journal of Ship Research, Vol. 25, June 1981, pp. 90-94.

The Economist, Science and Technology, Torpedo Junction, January 21st 2017.

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